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Use the Laws of Logarithms to combine the expression.

Use the Laws of Logarithms to combine the expression.
4 log x − (1/3)log(x2 + 1) + 5 log(x − 1)

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Shannon H. | Mathematics and Science TutorMathematics and Science Tutor
4.9 4.9 (340 lesson ratings) (340)
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Hi Jacob, so here how it goes,
                                                                                       Logarithmic Property
4logx - (1/3)log(x2 + 1) + 5log(x - 1)                                 rlogx = logxr
logx4 - log(x2 + 1)1/3 + log(x - 1)5                                   logM +logN = log MN, M=log(x2 + 1)1/3
                                                                                                                      N= log(x - 1)5
logx4 - log(x2+1)1/3(x-1)5                                                logM - logN = log(M/N), M= logx4
                                                                                                                       N= log(x2+1)1/3(x-1)5   
log( _____x4_________)
      log(x2+1)1/3(x-1)
 
Happy to help,
Shannon